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Properties

Label 475.3.bh
Level $475$
Weight $3$
Character orbit 475.bh
Rep. character $\chi_{475}(14,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2352$
Sturm bound $150$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.bh (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(150\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(475, [\chi])\).

Total New Old
Modular forms 2448 2448 0
Cusp forms 2352 2352 0
Eisenstein series 96 96 0

Trace form

\( 2352 q - 30 q^{2} - 30 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 45 q^{8} - 18 q^{9} + O(q^{10}) \) \( 2352 q - 30 q^{2} - 30 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 45 q^{8} - 18 q^{9} + 3 q^{10} + 36 q^{11} - 45 q^{12} - 30 q^{13} + 36 q^{14} - 93 q^{15} - 42 q^{16} - 30 q^{17} - 18 q^{19} - 66 q^{20} - 99 q^{21} + 90 q^{22} - 336 q^{24} + 342 q^{25} - 24 q^{26} - 45 q^{27} - 270 q^{28} + 72 q^{29} + 135 q^{30} - 27 q^{31} + 240 q^{33} - 18 q^{34} - 399 q^{35} - 144 q^{36} + 465 q^{38} - 36 q^{39} - 897 q^{40} - 18 q^{41} - 570 q^{42} - 114 q^{44} + 510 q^{45} - 1107 q^{46} - 150 q^{47} - 30 q^{48} + 7350 q^{49} - 819 q^{50} + 252 q^{51} + 30 q^{52} - 30 q^{53} + 156 q^{54} - 111 q^{55} + 300 q^{58} + 342 q^{59} - 729 q^{60} + 342 q^{61} + 1920 q^{62} - 765 q^{63} + 2007 q^{64} - 1656 q^{65} - 1194 q^{66} - 30 q^{67} - 27 q^{69} - 216 q^{70} + 1032 q^{71} - 1440 q^{72} - 30 q^{73} + 630 q^{74} - 48 q^{76} - 1530 q^{77} + 105 q^{78} - 378 q^{79} - 1389 q^{80} + 168 q^{81} - 975 q^{83} + 3213 q^{84} + 126 q^{85} - 468 q^{86} - 1455 q^{87} - 45 q^{88} - 198 q^{89} + 459 q^{90} - 459 q^{91} - 3240 q^{92} + 885 q^{95} - 804 q^{96} + 240 q^{97} + 255 q^{98} - 54 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.